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"""Tests for module Unbalanced OT with entropy regularization"""
# Author: Hicham Janati <hicham.janati@inria.fr>
#
# License: MIT License
import numpy as np
import ot
import pytest
from ot.unbalanced import barycenter_unbalanced
from scipy.special import logsumexp
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
def test_unbalanced_convergence(method):
# test generalized sinkhorn for unbalanced OT
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
a = ot.utils.unif(n)
# make dists unbalanced
b = ot.utils.unif(n) * 1.5
M = ot.dist(x, x)
epsilon = 1.
reg_m = 1.
G, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
reg_m=reg_m,
method=method,
log=True,
verbose=True)
loss = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
method=method,
verbose=True)
# check fixed point equations
# in log-domain
fi = reg_m / (reg_m + epsilon)
logb = np.log(b + 1e-16)
loga = np.log(a + 1e-16)
logKtu = logsumexp(log["logu"][None, :] - M.T / epsilon, axis=1)
logKv = logsumexp(log["logv"][None, :] - M / epsilon, axis=1)
v_final = fi * (logb - logKtu)
u_final = fi * (loga - logKv)
np.testing.assert_allclose(
u_final, log["logu"], atol=1e-05)
np.testing.assert_allclose(
v_final, log["logv"], atol=1e-05)
# check if sinkhorn_unbalanced2 returns the correct loss
np.testing.assert_allclose((G * M).sum(), loss, atol=1e-5)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
def test_unbalanced_multiple_inputs(method):
# test generalized sinkhorn for unbalanced OT
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
a = ot.utils.unif(n)
# make dists unbalanced
b = rng.rand(n, 2)
M = ot.dist(x, x)
epsilon = 1.
reg_m = 1.
loss, log = ot.unbalanced.sinkhorn_unbalanced(a, b, M, reg=epsilon,
reg_m=reg_m,
method=method,
log=True,
verbose=True)
# check fixed point equations
# in log-domain
fi = reg_m / (reg_m + epsilon)
logb = np.log(b + 1e-16)
loga = np.log(a + 1e-16)[:, None]
logKtu = logsumexp(log["logu"][:, None, :] - M[:, :, None] / epsilon,
axis=0)
logKv = logsumexp(log["logv"][None, :] - M[:, :, None] / epsilon, axis=1)
v_final = fi * (logb - logKtu)
u_final = fi * (loga - logKv)
np.testing.assert_allclose(
u_final, log["logu"], atol=1e-05)
np.testing.assert_allclose(
v_final, log["logv"], atol=1e-05)
assert len(loss) == b.shape[1]
def test_stabilized_vs_sinkhorn():
# test if stable version matches sinkhorn
n = 100
# Gaussian distributions
a = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std
b1 = ot.datasets.make_1D_gauss(n, m=60, s=8)
b2 = ot.datasets.make_1D_gauss(n, m=30, s=4)
# creating matrix A containing all distributions
b = np.vstack((b1, b2)).T
M = ot.utils.dist0(n)
M /= np.median(M)
epsilon = 0.1
reg_m = 1.
G, log = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, reg=epsilon,
method="sinkhorn_stabilized",
reg_m=reg_m,
log=True)
G2, log2 = ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
method="sinkhorn", log=True)
np.testing.assert_allclose(G, G2, atol=1e-5)
@pytest.mark.parametrize("method", ["sinkhorn", "sinkhorn_stabilized"])
def test_unbalanced_barycenter(method):
# test generalized sinkhorn for unbalanced OT barycenter
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
A = rng.rand(n, 2)
# make dists unbalanced
A = A * np.array([1, 2])[None, :]
M = ot.dist(x, x)
epsilon = 1.
reg_m = 1.
q, log = barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
method=method, log=True)
# check fixed point equations
fi = reg_m / (reg_m + epsilon)
logA = np.log(A + 1e-16)
logq = np.log(q + 1e-16)[:, None]
logKtu = logsumexp(log["logu"][:, None, :] - M[:, :, None] / epsilon,
axis=0)
logKv = logsumexp(log["logv"][None, :] - M[:, :, None] / epsilon, axis=1)
v_final = fi * (logq - logKtu)
u_final = fi * (logA - logKv)
np.testing.assert_allclose(
u_final, log["logu"], atol=1e-05)
np.testing.assert_allclose(
v_final, log["logv"], atol=1e-05)
def test_barycenter_stabilized_vs_sinkhorn():
# test generalized sinkhorn for unbalanced OT barycenter
n = 100
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
A = rng.rand(n, 2)
# make dists unbalanced
A = A * np.array([1, 4])[None, :]
M = ot.dist(x, x)
epsilon = 0.5
reg_m = 10
qstable, log = barycenter_unbalanced(A, M, reg=epsilon,
reg_m=reg_m, log=True,
tau=100,
method="sinkhorn_stabilized",
)
q, log = barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
method="sinkhorn",
log=True)
np.testing.assert_allclose(
q, qstable, atol=1e-05)
def test_implemented_methods():
IMPLEMENTED_METHODS = ['sinkhorn', 'sinkhorn_stabilized']
TO_BE_IMPLEMENTED_METHODS = ['sinkhorn_reg_scaling']
NOT_VALID_TOKENS = ['foo']
# test generalized sinkhorn for unbalanced OT barycenter
n = 3
rng = np.random.RandomState(42)
x = rng.randn(n, 2)
a = ot.utils.unif(n)
# make dists unbalanced
b = ot.utils.unif(n) * 1.5
A = rng.rand(n, 2)
M = ot.dist(x, x)
epsilon = 1.
reg_m = 1.
for method in IMPLEMENTED_METHODS:
ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, reg_m,
method=method)
ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
method=method)
barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
method=method)
with pytest.warns(UserWarning, match='not implemented'):
for method in set(TO_BE_IMPLEMENTED_METHODS):
ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, reg_m,
method=method)
ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
method=method)
barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
method=method)
with pytest.raises(ValueError):
for method in set(NOT_VALID_TOKENS):
ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, reg_m,
method=method)
ot.unbalanced.sinkhorn_unbalanced2(a, b, M, epsilon, reg_m,
method=method)
barycenter_unbalanced(A, M, reg=epsilon, reg_m=reg_m,
method=method)
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